# Thread: Substituting when figuring out limits...

1. ## Substituting when figuring out limits...

The question is find the limit as x approaches infinity, of x(e1/x -1)

The solution involves letting y = 1/x, however when substituting this in, the limit becomes x approaches 0.

What's the rules with changing the value approaching when substituting in limits, as this is not the first time I have seen this.

Thank you xxx

2. ## Re: Substituting when figuring out limits...

Originally Posted by princessp
The question is find the limit as x approaches infinity, of x(e1/x -1)

The solution involves letting y = 1/x, however when substituting this in, the limit becomes x approaches 0.

[b]No, as x approaches infinity, 1/x approaches 0 while staying positive. But y = 1/x, so it is y that is approaching 0 from the right,
that is, $0^+$.

What's the rules with changing the value approaching when substituting in limits, as this is not the first time I have seen this.
y = 1/x means x = 1/y

So,

$\displaystyle\lim_{x\to\infty}x(e^{1/x} - 1) \ =$

$\displaystyle\lim_{y\to\0^+}\tfrac{1}{y}(e^{y} - 1) \ =$

$\displaystyle\lim_{y\to\0^+}\dfrac{e^{y} - 1}{y}$